Explain whether or not a binomial distribution is a suitable model for the random variable.
(a) the number of tosses of a fair coin before the coin lands 'head'
(b) the score a pupil gets in answering 10 true/false questions with 1 mark for a correct answer and -1 for a wrong answer
(c) the number of rainy days in a randomly chosen week at a certain place for which weather records show that it rains on 40% of the days
(a) No. The number of trials if not fixed.
(b) No. If I let X be the number of questions answered correctly, then X~Bin(10,0.5)
but the marks obtained (Y) is given by Y=(1)X+(-1)(10-X)=2X-10 is NOT a binomial
(c) Maybe....the probability that probability that it rains might not be the same due to seasons.
Am I correct?